Solving Fuzzy Linear Programming Problems with Linear Membership Function

Authors : Rafail N. GASIMOV

Pages : 375-396

View : 15 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the ``modified subgradient method`` and use it for solving these problems. We also compare the new proposed method with well known ``fuzzy decisive set method``. Finally, we give illustrative examples and their numerical solutions.
Keywords : Fuzzy linear programming, fuzzy number, modified subgradient method, fuzzy decisive set method